"Train Sample Data-Driven Quantification of Quantum $k$-Entanglement via Machine Learning"

"This dataset is designed to support machine-learning research on multipartite quantum entanglement prediction. It contains randomly generated mixed quantum states together with their corresponding $k$-entanglement measures, enabling supervised learning of the functional mapping from a density matrix $\\rho$ to the entanglement measure $E_w^{(k,n)}(\\rho)$. The dataset covers nine representative multipartite qubit systems with qubit number not exceeding four, including $(2,2,2)_{k=2}$, $(2,2,2)_{k=3}$, $(2,4)_{k=2}$ for three-qubit systems and $(2,2,2,2)_{k=2}$, $(2,2,2,2)_{k=3}$, $(2,2,2,2)_{k=4}$, $(2,4,2)_{k=2}$, $(2,4,2)_{k=3}$, and $(2,8)_{k=2}$ for four-qubit systems. These structures correspond to multipartite systems with different partition configurations and effective local dimensions.For each system configuration, $30{,}000$ random mixed states are generated under the physical constraints of Hermiticity, unit trace, and positive semidefiniteness. Each dataset is divided into training and test subsets with an 80%\u201320% split. To ensure statistical comparability across different system structures, the sampling procedure maintains consistent distributions of entanglement degrees.The entanglement labels are computed using a highly accurate approximation algorithm based on a preconstructed entanglement-witness database. The released dataset includes quantum states stored in rho_data.npz and their corresponding entanglement labels stored in results.csv. This dataset provides a benchmark for studying machine-learning approaches to entanglement quantification and for analyzing how system size, partition structure, and local dimensions affect the difficulty of entanglement prediction."